Proceedings of CARI 2016

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Submitted on 2 Aug 2016

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l'Institut de Recherche pour le Développement (IRD), le Centre de coopération Internationale en Recherche

Agronomique pour le Développement (Cirad), le Centre International des Mathématiques Pures et

Appliquées (Cimpa), et l'Agence Universitaire de la Francophonie (AUF). Cette treizième édition, confiée à

l’Ecole Nationale d’Ingénieur de Tunis (ENIT), sous la coordination du professeur Nabil Gmati , a bénéficié

d’un large soutien des institutions universitaires suivantes : la Faculté des Sciences de Tunis (FST), l’Ecole

Polytechnique de Tunisie (EPT), l’Ecole Nationale Supérieure d’Informatique (ENSI), l’Ecole Supérieure

privée d’Ingénierie et de Technologies (ESPRIT) et de l’Ecole Supérieure des Télécommunications

(Sup’Com). Quatre universités du grand Tunis se sont également associées pour la réussite de cette nouvelle

édition du colloque : l’Université Tunis El Manar (UTM), l’Université de la Manouba (UM), l’Université de

Carthage (UC), l’Université Virtuelle de Tunis (UVT). Ces universités regroupent l'essentiel des institutions

scientifiques du grand Tunis. Le CARI a également bénéficié du soutient de l’Institut Français de Tunisie

(IFT).

Le CARI est devenu un lieu privilégié de rencontre et d’échanges de chercheurs et décideurs africains et

internationaux de haut niveau dans les domaines de l’informatique et des mathématiques appliquées. Le

programme scientifique, qui reflète la richesse et la diversité de la recherche menée sur le continent africain,

met un accent particulier sur les travaux susceptibles de contribuer au développement technologique, à la

connaissance de l'environnement et à la gestion des ressources naturelles. Ce programme se décline en 51

communications scientifiques, sélectionnées parmi 130 articles soumis, et des conférences invitées

présentées par des spécialistes de renommée internationale.

L’Ecole de recherche Cimpa, qui a porté cette année sur

sur les « mathématiques de la biologie »,

remplace

désormais les traditionnels tutoriels organisés en marge du

CARI

.

Bien plus qu'un simple colloque, le CARI est un cadre dynamique de coopération, visant à rompre l'isolement

et à renforcer la communauté scientifique africaine. Toute cette activité repose sur l'action forte et efficace de

beaucoup d'acteurs. Nous remercions tous nos collègues qui ont marqué leur intérêt dans le CARI

en y

soumettant leurs travaux scientifiques, les relecteurs qui ont accepté d’évaluer ces contributions et les

membres du Comité de programme qui ont opéré à la sélection des articles. L’ensemble des activités liées au

CARI sont répertoriées sur le site officiel du CARI

(

http://www.cari-info.org/

) maintenu par l’équipe du

professeur Mokhtar Sellami de l’université d’Annaba. Laura Norcy, d'Inria, a apporté son soutien pour la

coordination de cette manifestation. L’organisation du colloque a reposé sur le comité local d'organisation,

mis en place par le professeur Nabil Gmati.

Que les différentes institutions, qui, par leur engagement financier et par la participation de leurs membres,

apportent leur soutien, soient également remerciées, et, bien sûr, toutes les institutions précédemment citées,

qui soutiennent le CARI au fil de ses éditions.

Pour les organisateurs

Moussa Lo, Président du CARI

Eric Badouel, Secrétaire du Comité permanent du CARI

Nabil Gmati, Organisateur du CARI 2016

the Institut de Recherche pour le Développement (IRD), the Centre de coopération Internationale en

Recherche Agronomique pour le Développement (Cirad), the International Center for Pure and Applied

Mathematics (ICPAM) and the Agence Universitaire de la Francophonie (AUF). This thirteenth edition,

entrusted to ENIT (Ecole Nationale d’Ingénieurs de Tunis), under the coordination of Professor Nabil Gmati,

has profited from a generous support of the following academic institutions: Faculté des Sciences de Tunis

(FST), Ecole Polytechnique de Tunisie (EPT), Ecole Nationale Supérieure d’Informatique (ENSI), Ecole

Supérieure privée d’Ingénierie et de Technologies (ESPRIT) and Ecole Supérieure des Télécommunications

(Sup’Com). Four universities of the greater Tunis, which are the main scientific institutions of Tunis, also

joined for the success of CARI: University of Tunis El Manar (UTM), La Manouba University (UM),

University of Carthage (UC), Université Virtuelle de Tunis (UVT).

CARI also acknowledge supports from the Institut Français de Tunisie ( IFT).

CARI has evolved into an internationally recognized event in Computer Science and Applied Mathematics.

The scientific program, which reflects the richness and the diversity of the research undertaken on the

African continent with a special emphasis on works related to the development of new technologies,

knowledge in environmental sciences and to the management of natural resources, consists of 51 scientific

contributions, selected from 130 submissions, together with invited talks delivered by acknowledged

specialists.

From now on, the tutorials that used to precede the CARI are replaced by a CIMPA-ICPAM Research school

that puts a focus on some particular topic relevant to CARI’s community. For this edition the research school

was dedicated to the “Mathematics for Biology”.

More than a scientific gathering, CARI is also a dynamic environment for cooperation that brings together

African researchers with the end result to break the gap of isolation. The successes of such an initiative rely

on the contribution of many actors. We wish first to thank our colleagues who showed their interest in CARI

by submitting a paper, the referees who accepted to evaluate these contributions, and the members of the

Program Committee who managed the selection of papers. This process rested on the CARI official site

(http://www.cari-info.org/) maintained by the team of professor Mokhtar Sellami at the University of

Annaba. Laura Norcy, from Inria, was involved in numerous activities for the coordination of the Event. The

local organization has been handled by the local organization committee under the supervision of professor

Nabil Gmati.

Thanks also for all the institutions that support and provide funding for CARI conferences and related

activities, and all the institutions involved in the organization of the conference.

For the organizing committee

Moussa Lo, Chairman of CARI

Eric Badouel, Secretary of CARI Permanent Committee

Nabil Gmati, Chair of CARI 2016

Ezzine ABDELHAk, ENSAT, Morocco

Olivier ALATA, Univ. Saint-Etienne, France

Tarik Boujiha, Univ. ibn tofail-kénitra, Morocco

Mohamed DAOUDI, Telecom Lille/LIFL, France

Denis HAMAD, Univ. du Littoral Côte d'Opale, France

Ahmed HAMMOUCH, CNRST, Morocco

Lloussaine MASMOUDI, Univ. Mohammed V, Rabat, Morocco

Ahmed MOUSSA, LabTIC ENSAT, Morocco

Rachid OULAD HAJ THAMI, ENSIAS, Marocco

Abderrahmane SBIHI, ENSA Tanger, Morocco

Raja Touahni, Université Ibn Tofail, Morocco

Lynda ZAOUI, Oran University, Algeria

Djemel ZIOU, Sherbrooke University, Canada

Calcul scientifique et parallélisme / Scientific Computing and Parallelism

Jocelyne ERHEL, Inria, France

El Mostafa DAOUDI, Univ. Mohamed I, Oujda, Morocco

Laurent DEBREU, Inria, France

Laura GRIGORI, Inria, France

Abdou GUERMOUCHE, Univ. Bordeaux, France

Pierre MANNEBACK, University of Mons, Belgium

Maher MOAKHER, Ecole Nationale d'Ingénieurs de Tunis, Tunisia

Yanik NGOKO, Univ. Paris 13, France

Boniface NKONGA, University of Nice-Sophia-Antipolis

Patrice QUINTON, ENS Rennes, France

Denis TRYSTRAM, Grenoble Institute of Technologu, France

Intelligence artificielle et environnements informatique pour l'apprentissage humain / Artificial Intelligence and Computer-based Collaborative Environmental

Meziane AIDER, USTHB, Algeria

Djamil AISSANI, Univ. Bejala, Algeria

Monique BARON, Sorbonne UPMC, Lip6, France

Mahieddine DJOUDI, Poitiers University, France

Abdellatif ENNAJI, Univ. Rouen, France

Mokhtar SELLAMI, Annaba University, Algeria

Hassina SERIDI, Annaba University,, Algeria

Christophe SIBERTIN-BLANC, Irit, France

Salvatore TABBONE, Univ. de Lorraine, France

François VERNADAT, LAAS-CNRS, Toulouse, France

Extraction et Organisation des Connaissances / Knowledge Organization and Mining

Hugo ALATRISTA-SALAS, Pontificia Universidad Catolica del Peru

Jérôme AZE, LIRMM, University of Montpellier 2, France

Nicolas BECHET, Université de Bretagne Sud

Hacene BELHADEF, University of Constantine, Algeria

Béatrice BOUCHOU MARKHOFF, Univ. François Rabelais de Tours, France

Ibrahim BOUNHAS, LISI, Carthage University, Tunisia

Sandra BRINGAY, LIRMM, University Paul Valéry, France

Patrice BUCHE, Supagro INRA, France

Gaoussou CAMARA, Univ. Alioune Diop, Bambey, Senegal

Célia DA COSTA TEREIRA, Univ. Nice Sophia Antipolis, France

Cheikh Taliboula DIOP, UGB, Saint-Louis, Senegal

Bilel ELAYEB, ENSI, Tunisia

Dino IENCO, IRSTEA, France

Clement JONQUET, LIRMM, University of Montpellier 2, France

Eric KERGOSIEN, University of Lille, France

Philippe LEMOISSON, TETIS, Cirad, France

Moussa LO, Univ. Gaston Berger, Senegal

Cédric LOPEZ, Viseo Research Center, France

Isabelle MOUGENOT, Espace-Dev, University of Montpellier 2, France

Mathieu ROCHE, TETIS, Cirad, France

Fatiha SAIS, LRI, Paris Sud University, France

Hassan SANEIFAR, Raja University, Iran

Joël SOR, Cirad, France

Maguelonne TEISSEIRE, TETIS, Irstea, France

Systèmes distribués et réseaux / Distributed systems and networks

Soraya AIT CHELLOUCHE, University of Rennes, France

Olivier BARAIS, University of Rennes, France

Melhem EL HELOU, Univ. Saint-Joseph de Beyrouth, Lebanon

Davide FREY, Inria Rennes, France

Abdoulaye GAMATIE, LIRMM, France

Bamba GUEYE, UCAD, Dakar, Senegal

Jean-Claude HOCHON, Airbus SAS, France

Michel HURFIN, Inria Rennes, France

Marc IBRAHIM, Saint-Joseph University, Lebanon

Samer LAHOUD, University of Rennes, France

Maryline LAURENT, Telecom Sud-Paris, France

Moussa LO, Univ. Gaston Berger, Senegal

Pascal LORENZ, Univ. Haute Alsace, France

Stéphane MAAG, Telecom Sud-Paris, France

Ludovic ME, Supélec Rennes, France

Fethi Bin Muhammad BELGACEM, PAAET, Kuwait

Monia BELLALOUNA, ENSI, Tunisia

Hend BEN AMEUR, LAMSIN-ENIT and IPEST, Tunisia

Faker BEN BELGACEM

, UTC Compiègne, France

Slimane BEN MILED, University Tunis el Manar, Tunisia

Adel BLOUZA, University of Rouen, France

Fabien CAMPILLO, Inria, France

Nicolas CHAMPAGNAT, Inria, France

Nadia CHOULAIEB, ENIT, Tunisia

Jean CLAIRAMBAULT, Inria Paris- LJLL, UMPC, France

Yves DUMONT, Cirad, France

Radhouene FEKIH SALEM, University of Monastir, Tunisia

Jean-Frédéric GERBEAU, Inria, France

Nabil GMATI, LAMSIN-ENIT, Tunisia

Lamia GUELLOUZ, ENIT, Tunisia

Abderrahmane HABBAL, University of Nice-Inria, France

Ridha HAMBLI, Polytech Orleans, France

Nejla HARIGA-TATLI, INAT-LAMSIN, Tunisia

Yousri HENCHIRI, University of Montpellier 2, France

Abderrahman IGGIDR, Inria, France

Adil KHALIL, University of Marrakech, Morocco

Michel LANGLAIS, University of Bordeaux, France

Claude LOBRY, University of Nice, France

John MADDOCKS, EPFL, Switzerland

Sylvie MELEARD, Ecole Plotechnique, France

Ali MOUSSAOUI, Tlemcen University, Algeria

Tri NGUYEN-HU, IRD, France

Gauthier SALLET, Université de Lorraine, Nancy, France

Tewfik SARI, IRSTEA, Montpellier, France

Suzanne TOUZEAU, INRA-Inria, France

Hatem ZAAG, University Paris 13, France

Nejib ZEMZEMI, Inria, France

Pascal A

NDRE

Julien

A

RINO

Abdon A

TANGANA

Mejdi A

ZAIEZ

Jérôme A

ZE

Eric B

ADOUEL

Olivier

B

ARAIS

Kamel B

ARKAOUI

Monique B

ARON

Nicolas

B

ECHET

Fethi Bin Muhammad

BELGACEM

Hacene

B

ELHADEF

Monia B

ELLALOUNA

Hend B

EN

A

MEUR

Faker B

EN

B

ELGACEM

Slimane B

EN

M

ILED

Fethi B

IN

M

UHAMMAD

B

ELGACEM

Adel B

LOUZA

Béatrice B

OUCHOU

M

ARKHOFF

Tarik B

OUJIHA

Ibrahim

B

OUNHAS

Sandra B

RINGAY

Patrice B

UCHE

Fabien C

AMPILLO

Gaoussou C

AMARA

Jérôme C

ANALS

Bernard C

AZELLES

Nicolas C

HAMPAGNAT

François

C

HAROY

Nadia CHOULAIEB

Jean C

LAIRAMBAULT

Célia

DA

C

OSTA

P

EREIRA

El Mostafa Daoudi

Mohamed D

AOUDI

Laurent D

EBREU

Cheikh Talibouya D

IOP

Aissani D

JAMIL

Davide

F

REY

Yles F

ALCONE

Christian F

OTSING

Abdoulaye G

AMATIE

Jean-Frédéric G

ERBEAU

Nabil G

MATI

Arnaud G

RIGNARD

Laura G

RIGORI

Lamia GUELLOUZ

Bamba

G

UEYE

Abdou G

UERMOUCHE

Abderrahmane H

ABBAL

Kais H

ADDAR

Denis H

AMAD

Ridha HAMBLI

Ahmed H

AMMOUCH

Nejla

H

ARIGA

-T

ATLI

Seridi H

ASSINA

Yousri H

ENCHIRI

Jean-Claude H

OCHON

Michel H

URFIN

Marc

I

BRAHIM

Dino I

ENCO

Abderrahman I

GGIDR

Clement J

ONQUET

Eric K

ERGOSIEN

Adil K

HALIL

Georges-Edouard

K

OUAMOU

Samer L

AHOUD

Michel L

ANGLAIS

Maryline L

AURENT

Philippe L

EMOISSON

Christophe L

ETT

Moussa L

O

Claude L

OBRY

Cédric L

OPEZ

Pascal L

ORENZ

Stéphane M

AAG

John MADDOCKS

Isabelle M

OUGENOT

Ahmed M

OUSSA

Ali M

OUSSAOUI

Yanik N

GOKO

Tri N

GUYEN

-H

UU

Boniface N

KONGA

Rachid O

ULAD

H

AJ

T

HAMI

Congduc P

HAM

Patrice Q

UINTON

Damien R

OBERT

Benjamin R

OCHE

Mathieu R

OCHE

Pierre R

OLIN

Gauthier

S

ALLET

Abed Ellatif S

AMHAT

H

ASSAN

S

ANEIFAR

Tewfik

S

ARI

Abderrahmane S

BIHI

Christophe S

IBERTIN

-B

LANC

Fathia S

AIS

Idrissa S

ARR

Mokhtar S

ELLAMI

William S

HU

Yahya S

LIMANI

Joël S

OR

Salvatore T

ABBONE

Claude T

ANGHA

Maguelonne T

EISSEIRE

Ousmane T

HIARE

Raja T

OUAHN

i

Suzanne T

OUZEAU

Denis T

RYSTRAM

François V

ERNARDAT

César V

IHO

Hatem Z

AAG

Lynda Z

AOUI

Nejib ZEMZEMI

Djemel Z

IOU

Nesrine Kalboussi, Jérôme Harmand, Nihel Ben Amar, F. Ellouze ... 16 – 26

Well’s location in porous media using topological asymptotic expansion

Wafa Mansouri, Thouraya Nouri Baranger, Hend Ben Ameur, Nejla Tlatli ... 27 – 34

Data assimilation for coupled models. Toward variational data assimilation for coupled models: first experiments on a diffusion problem

Rémi Pellerej, Arthur Vidard, Florian Lemarié ... 35 – 42

Calcul numérique de solutions de l'équation de Schrödinger non linéaire faiblement amortie avec défaut

Laurent Di Menza, Olivier Goubet, Emna Hamraoui, Ezzeddine Zahrouni ... 43 – 53

Towards a recommender system for healthy nutrition. An automatic planning-based approach

Yanik Ngoko ... 54 – 62

Algorithmes hybrides pour la résolution du problème du voyageur de commerce

Baudoin Tsofack Nguimeya, Mathurin Soh, Laure Pauline Fotso ... 63 – 74

A systematic approach to derive navigation model from data model in web information systems

Mohamed Tahar Kimour, Yassad-Mokhtari Safia ... 75 – 83

Réconciliation par consensus des mises à jour des répliques partielles d’un document structuré

Maurice Tchoupé Tchendji, William M. Zekeng Ndadji ... 84 – 96

Un dépliage par processus pour calculer le préfixe complet des réseaux de Petri

Médésu Sogbohossou, Antoine Vianou ………... 97 – 108

Modeling User Interactions in Dynamic Collaborative Processes using Active Workspaces

Robert Fondze Jr Nsaibirni, Gaëtan Texier ………... 109 – 116

On Distributing Bayesian Personalized Ranking from Implicit Feedback

Modou Gueye ………... 117 – 125

Requêtes XPath avec préférences structurelles et évaluations à l'aide d'automates

Maurice Tchoupé Tchendji, Brice Nguefack ... 126 – 137

Empirical study of LDA for Arabic topic identification

Marwa Naili, Anja Habacha Chaibi, Henda Ben Ghézala ... 138 – 145

Approche hybride pour le développement d’un lemmatiseur pour la langue arabe

Mohamed Boudchiche, Azzeddine Mazroui ... 146 – 153

Overview of the social information’s usage in information retrieval and recommendation systems

Abir Gorrab, Ferihane Kboubi, Henda Ben Ghezala ... 154 – 161

Vers un système iconique d’aide à la décision pour les praticiens de la médecine traditionnelle

Linear Token-Based MAC protocol for linear sensor network

El Hadji Malick Ndoye, Ibrahima Niang, Frédérique Jacquet, Michel Misson ... 215 – 222

Méthode Tabou d'allocation des slots de fréquence requis sur chaque lien d’un réseau optique flexible

Beman Hamidja Kamagaté, Michel Babri, Bi Tra Gooré, Konan Marcelin Brou ... 223 – 232

Evidential HMM Based Facial Expression Recognition in Medical Videos

Arnaud Ahouandjinou, Eugène C. Ezin, Koukou Assogba, Cina Motamed, Mikael A. Mousse,

Bethel C.A.R.K. Atohoun ... 233 – 242

Tatouage vidéo dynamique et robuste basé sur l’insertion multi-fréquentielle

Sabrine Mourou, Asma Kerbiche, Ezzedine Zagoubra ... 243 – 251

Dynamic Pruning for Tree-based Ensembles

Mostafa El Habib Daho, Mohammed El Amine Lazouni, Mohammed Amine Chikh ... 252 – 261

Fast Polygons Fusion for Multi-Views Moving Object Detection from Overlapping Cameras

Mikaël Ange Mousse, Cina Motamed, Eugène C. Ezin ... 262 – 268

A multi-agent model based on Tabu Search for the permutation flow shop problem minimizing total flowtime

Soumaya Ben Arfa, Olfa Belkahla Driss ... 269 – 276

Formation de coalitions A-core: S-NRB

Pascal François Faye, Mbaye Sene, Samir Aknine ... 277 – 288

Towards an intelligent prognostic approach based on data mining and knowledge management

Safa Ben Salah, Imtiez Fliss, Moncef Tagina ... 289 – 299

Amélioration de la visite de classe de l’enseignement technique : intégration d’un dispositif de médiation

Frédéric T. Ouédraogo, Daouda Sawadogo, Solange Traoré, Olivier Tindano ... 300 – 311

Efficient high order schemes for stiff ODEs in cardiac electrophysiology

Charlie Douanla Lontsi, Yves Coudière, Charles Pierre ... 312 – 319

A model of flocculation in the chemostat

Radhouane Fekih-Salem, Tewik Sari ... 320 – 331

Modeling the dynamics of cell-sheet:

Fisher-KPP equation to study some predictions on the injured Cell sheet

Mekki Ayadi, Tunisia, Abderahmane Habbal, Boutheina Yahyaoui ... 332 – 343

Global weak solution to a 3D Kazhikhov-Smagulov model with Korteweg stress

Valaire Yatat Djeumen, Jean-Jules Tewa, Samuel Bowong ... 383 – 392

Identification of Robin coefficient for Stokes Problem

Amel Ben Abda, Faten Khayat ... 393 – 401

Schistosomia infection: A mathematical analysis of a model with mating structure

Mouhamadou Diaby, Abderrahman Iggidr ... 402 – 411

Analyzing a two strain infectious disease

Otto Adamou, M’hammed El Kahoui, Marie-Françoise Roy, Thierry Van Effelterre ... 412 – 423

Sensitivity of the electrocardiographic forward problem to the heart potential measurement noise and conductivity uncertainties

Rajae Aboulaich, Najib Fikal, El Mahdi El Guarmah, Nejib Zemzemi ... 424 – 431

Hopf bifurcation properties of a delayed predator-prey model with threshold prey harvesting

Israël Chedjou Tankam, Plaire Tchinda Mouofo, Jean Jules Tewa ... 432 – 443

Optimal Control of Arboviral Diseases

Hamadjam Abboubakar, Jean Claude Kamgang ... 444 – 455

Identification of self-heating effects on the behaviour of HEMA-EGDMA hydrogels biomaterials using non-linear thermo-mechanical modeling

Nirina Santatriniaina, Mohamadreza Nassajian Moghadam, Dominique Pioletti, Lalaonirina Rakotomanana

... 456 – 473

Mathematical modeling of climate change on tick population dynamics

Leila Khouaja, Slimane Ben Miled, Hassan Hbid ... 474 – 483

Stochastic modeling of the anaeorobic model AM2b: Models at different scales

Fabien Campillo , Mohsen Chebbi, Salwa Toumi,... 484 – 493

Identification of source for the bidomain equation using topological gradient

a _{Instituto Nacional de Investigacao Pesqueira, Av. Mao Tse Tung 309, Maputo, Mozambique}

dinomalawene@yahoo.com.br or MLNBER003@myuct.ac.za

b _{Biological Sciences Dept. and Marine Research Institute, University of Cape Town, Private Bag}

X3, Rondebosch 7701, South Africa.

c _{Nelson Mandela Metropolitan University, Port Elizabeth, South Africa}

d _{Institut de Recherche pour le Développement, UMI 209, Centre de Recherche Halieutique}

Méditerranéenne et Tropicale, Avenue Jean Monnet - BP 171 - 34203 Sète Cedex, France.

e _{Institut de Recherche pour le Développement, Centre IRB de Bretagne, B.P. 70 – 29280,}

Plouzane, France.

f _{Institut de Recherche pour le Développement, UMR 248, Centre de Recherche Halieutique}

Méditerranéenne et Tropicale, Avenue Jean Monnet - BP 171 - 34203 Sète Cedex, France.

ABSTRACT. The Sofala Bank supports an important penaeid shrimps fishery where Penaeus

indicus and Metapenaeus monoceros (banana shrimp) are the two main target species. The

purpose of the present paper is to investigate the roles of biophysical processes on transport of larvae of banana shrimps on the Sofala Bank. A high-resolution two-way nested Regional Ocean Modeling System (ROMS) of the Sofala Bank is developed. The ROMS solution agrees well with available observations and literature. An individual-based model (IBM) using Ichthyop coupled to the ROMS outputs is developed for the banana shrimps larvae on the bank. Simulated larval transport are influenced by the offshore mesoscale eddy activity.

1. Introduction

The Sofala Bank is located within 16o _{S (near Angoche) and 21}o _{S (Bazaruto}

archipelago) on the western side of the Mozambique Channel between Madagascar and the African mainland. The continental shelf is generally wide and shallow, with an average depth 20-30 m. The bank is a key habitat for the shallower water penaeid shrimps in the Southwest Indian Ocean (Ivanov and Hassan, 1976). It supports an important multi-sector and multi-species shrimp fishery. The two most important species are the closely related Penaeus indicus and Metapenaeus monoceros (so-called “banana shrimps) that contribute > 80 % of the total catch (de Sousa et al., 2008). The catch has been declining from >7000 tons in 2004 – 2006 to a low level of ~ 2000 tons in 2012 (de Sousa et al., 2013). This decrease is thought to be related to a combination of detrimental environmental factors and overfishing (de Sousa et al., 2013). However, no conclusive evidence of either overfishing or environmental factors has been found on the Sofala Bank.

Shrimp catch depends to a large extent on recruitment of juveniles into the fishery. This is driven by environmental factors that influence larval transport and dispersal (Ehrhardt and Legault, 1999). It is known that banana shrimps on the Sofala Bank spawn all year round (de Sousa et al., 2008; Malauene 2015) and their eggs develop to first postlarvae within 15 days (i.e. passive pelagic larval duration – PLD). During such PLD currents can transport shrimp larvae either shoreward or offshore (Penn, 1975).

The Mozambique Channel circulation is dominated by mesoscale

eddies and rings. These eddies, and particularly dipole eddies, can generate high velocity offshore-directed boundary currents (Roberts et al., 2014). Many studies have shown that eddy-induced currents can transport coastal biotic and abiotic material offshore (Tew-Kai and Marsac, 2009; Malauene et al., 2014). It is hypothesized that shrimp larvae similarly can be transported to offshore regions where they are unable to survive. The aim of this paper is to investigate the interactive roles of biophysical processes on transport of the banana shrimp larvae in tropical, shallow waters of the Sofala Bank. In the presence of limited observational data the present study is mostly based in numerical models.

2. Model and data

2.1. Hydrodynamic ROMS model for ocean circulation

The Regional Ocean Modeling System (ROMS) is a three-dimensional, split-explicit, free-surface, topography-following vertical and horizontal sigma-coordinate ocean model (Shchepetkin and McWilliams, 2005). The ROMS_AGRIF used in this study uses a fourth-order advection scheme, which reduces dispersive property errors and enhances model resolution of smaller scale processes.

A model domain encompasses the entire Sofala Bank and the offshore adjacent waters between roughly 14 – 24o _{S. The model uses a structured regular square grid in}

the horizontal plane with 6.36 km (1\16o_{) resolution for the large, i.e. parent grid. For a}

better representation of small-scale coastal features a second fine grid was created using two-way nesting (Debreu et al., 2012); the child grid at 2.12 km (1\48o_{) resolution.}

The model topography was derived from the General Bathymetric Chart of the Oceans (GEBCO) One Minute Grid data set (available at

http://www.gebco.net/data_and_products/gridded_bathymetry_data/) and interpolated to the parent and child grid. Both parent and child grid has 50 vertical sigma-layers.

For surface forcing monthly climatologies are used. Sea surface wind stress from the Quick Scatterometer (QuikSCAT) satellite at a grid resolution of 1\2o_{. Surface}

fresh-water and heat fluxes from Comprehensive Ocean-Atmosphere Data Set (COADS) also at 1\2o _{resolution. Sea surface temperature (SST) from Pathfinder satellite observations}

at 9 km resolution.

The lateral boundaries of the model domain are open everywhere except at the coast. For the lateral open boundary conditions it was used outputs from the South-West Indian ocean Model (SWIM, Halo et al. 2014) applying the one-way nesting technique (Mason et al., 2010). Tides (ten constituents M2, S2, N2, K2, K1, O1, P1, Q1, Mf and Mm) at 1/4o _{resolution from the Global Inverse Tide Model data set (TPXO6.2) were}

also integrated into the model boundaries.

Four rivers Licungo, Zambezi, Pungue and Buzi that drain into the Sofala Bank were considered in one model experiment. Rivers were included as point sources of tracers (temperature and salinity) and momentum (realistic river flow) made available in monthly climatology by the Mozambican National Directorate of Water.

2.2. Individual-based model for larval transport

Individual-based model (IBM) is used here to simulate transport of banana shrimp larvae on the Sofala Bank. The IBM simulations were developed using Ichthyop version 3.1 (Lett et al., 2008, available at http://www.ichthyop.org) coupled to the nested ROMS model of the Sofala Bank. Ichthyop is a Lagrangian transport tool that tracks the trajectories of virtual eggs and larvae providing information of their state: position (longitude, latitude and depth), age (days) and status (alive or dead) at each time step.

Nine release areas (including spawning and non-spawning locations) were defined for the IBM simulations, based in the actual spawning locations for banana shrimp on the Sofala Bank identified by Malauene (2015). Simulations consisted of randomly releasing 30000 virtual banana shrimp eggs within the release areas every three days for five years and tracking their trajectories for 15 days (PLD). During this period simulated larvae could either stay on the bank (considered as successfully retained) or transported out (considered as lost).

2.3. Altimetry data

To evaluate the model ability to reproduce the mesoscale eddy activity, weekly “Delayed Time – DT” mapped absolute dynamic topography (MADT) at grid resolution of 1/4o _{from 1993 to 1999 data were used. The data combine sea surface height (SSH)}

observations merged from multi-satellite (TOPEX/Poseidon, Jason-1, GFO, ERS-1, ERS-2 and ENVISAT) altimeter missions processed by SSALTO/Duacs and distributed by AVISO with support from Centre National d'Etudes Spatiales (CNES, http://www.aviso.oceanobs.com), hereafter refereed to as AVISO observations.

3. Results

3.1 Simulated eddies variability, circulation and structure

The model sea surface height (SSH) and the AVISO altimetry agree reasonable well (Fig. 1A and B), in particular, the high mean SSH from the northernmost limit down the channel, the offshore low SSH centered at ~22o _{S and ~40}o _{E, and the}

west-east SSH gradient over the slope following the bathymetry between 200 and 2000 m depth. A similar strong slope mean SSH gradient was found in another model study of the Mozambique Channel (Quartly et al., 2013).

Mean eddy kinetic energy (EKE) computed from the model SSH and from AVISO observations are in qualitative agreement (Fig. 1C and D), especially, the two centers of maximum energy one between 21-22o _{S and 38}o _{E and the other between 19-20}o _{S and}

39o _{E. Quantitatively, the model energy doubled that of AVISO observations,}

suggesting that the model overestimated EKE by some ~50 %.

Figure 1 : Comparison between mean SSH (A) derived from ROMS years 4-10, (B) mean absolute dynamic topography derived from AVISO between 1993-1999. And mean EKE (cm2_s-1_{) from (C) the model and (D) AVISO. Pink lines indicate the 200}

3.2 Simulated patterns of the banana shrimp larval transport

Simulated larvae density distribution indicated that larvae were found all over the model domain, with the high concentration on the shelf of the Sofala Bank, but some exited the bank (not shown). Snapshots of trajectories of simulated larvae show that most of the path of the larvae transported out of the bank display a circular shame (Fig. 2A, B and C), supporting the influence of the Mozambique channel eddies in advecting the banana shrimp larvae (Malauene 2015). In other cases, as depicted in Fig. 2D, nearly all larvae stayed on the bank for the full duration of the simulation. This coincided with period of weak or calm Mozambique Channel eddy activity (Malauene 2015). It is apparent that larvae originated from the southern release areas off Beira move little (Fig. 2A-D).

Figure 3 : Snapshots of trajectories of simulated larvae originated from the northern (red), central (green) and southern (blue) release areas. For green and blue releases areas, dark colors indicate inshore and light offshore. for simulations starting: (A) 2 February, (B) 21 March, (C) 3 June and (D) 5 July.

4. Discusion

The strong west-east gradient of mean SSH apparent over the Mozambican continental slope between the 200 and 2000 m isobaths in both the model and AVISO observations is an indication of the presence of a mean “Mozambique Current”. The model current, however, was stronger than that observed from AVISO. This probably because of the high-resolution (~6 km) of the model compared to the global, smoothing and coarser resolution (~25 km) of AVISO observations (Quartly et al., 2013).

The model overestimation of the mean EKE and thus the mean eddy variability in about 50% is gained from the SWIM climatology model used here for the lateral open boundary conditions. The elevated mean EKE from the model and AVISO, however, occurred at the same place, indicating that the model reproduce the Mozambique Channel eddy variability. According to Halo et al. (2014), the SWIM model overestimated the Mozambique Channel eddy variability relative to AVISO by about 40-50 % probably because SWIM reproduces the eddies with larger diameter and higher amplitude than AVISO.

The present study shows that the offshore highly energetic eddies of the Mozambique Channel strongly influence the Sofala Bank circulation and river plume direction. The direction and magnitude of the eddy impact depend on the eddy type, strength and proximity to the shelf. Offshore eddies have little impact on the dominant tidal region off Beira.

Offshore eddies influence the pattern of simulated larval transport on the Sofala Bank except off Beira Bay. Bay of Beira is semi-enclosed and thus protected from the impact of these eddies. Generally in the absence of mesoscale eddy activity larvae stay in the Sofala Bank. Eddies therefore are unlikely to produce a continuous declining in the catch.

5. Reference

de Sousa, L. P., Abdula, S., de Sousa, B. P., Penn, J., and Howell, D. (2013). The shallow water shrimp at Sofala Bank Mozambique 2013. Unpublished report Instituto Nacional de Investigação Pesqueira, Maputo.

de Sousa, L. P., Brito, A., Abdula, S., Penn, J., and Howell, D. (2008). O Camarao do Banco e Sofala 2008. Unpublished report Instituto Nacional de Investigação Pesqueira, Maputo. (In Portuguese).

Debreu, L., Marchesiello, P., Penven, P., and Cambon, G. (2012). Two-way nesting in split-explicit ocean models: Algorithms, implementation and validation. Ocean Modelling, 49 – 50:1 – 21.

Ehrhardt, N. M. and Legault, C. M. (1999). Pink Shrimp, Farfantepenaeus duorarum, Recruitment Variability as an Indicator of Florida Bay Dynamics. Estuaries, 22(2):pp. 471 – 483.

Halo, I., Backeberg, B., Penven, P., Ansorge, I., Reason, C., and Ullgren, J. E. (2014). Eddy properties in the Mozambique Channel: A comparison between observations and two numerical ocean circulation models. Deep Sea Research Part II: Topical Studies in Oceanography, 100(0):38 – 53.

Ivanov, B. G. and Hassan, A. M. (1976). Penaeid Shrimps (Decapoda, Penaeidae) Collected of East Africa by the Fishing Vessel "Van Gogh", 1. Solenocera ramadani sp. nov., and Commercial Species of the Genera Penaeus and Metapenaeus. Crustaceana, 30(3):241 – 251.

Lett, C., Verley, P., Mullon, C., Parada, C., Brochier, T., Penven, P., and Blanke, B. (2008). A Langrangian tool for modelling ichthyoplankton dynamics. Enviromental Modelling & Software, 23:1210 – 1214.

Malauene, B. S., Shillington, F. A., Roberts, M. J., and Moloney, C. L. (2014). Cool, elevated chlorophyll-a waters off northern Mozambique. Deep Sea Research Part II: Topical Studies in Oceanography, 100(0):68 – 78.

Malauene, B. S. (2015). Environmental influences on the banana shrimps of the Sofala Bank, Mozambique Channel. PhD thesis, Department of Biological Sciences - University of Cape Town, South Africa.

Mason, E., Molemaker, J., Shchepetkin, A. F., Colas, F., McWilliams, J. C., and Sangra, P. (2010). Procedures for offine grid nesting in regional ocean models. Ocean Modelling, 35(1-2):1 – 15.

Penn, J. W. (1975). The influence of tidal cycles on the distributional pathway of Penaeus latisulcatus Kishinouye in Shark Bay, Western Australia. Australian Journal of Marine and Freshwater Research, 26:93 – 102.

Quartly, G., de Cuevas, B., and Coward, A. (2013). Mozambique channel eddies in GCMS: A question of resolution and slippage. Ocean Modelling, 63(0):56 – 67.

Roberts, M. J., Ternon, J.-F., and Morris, T. (2014). Interaction of dipole eddies with the western continental slope of the Mozambique Channel. Deep Sea Research Part II: Topical Studies in Oceanography, 100(0):54 – 67.

Shchepetkin, A. F. and McWilliams, J. C. (2005). The regional ocean modeling system (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Modell., 9:347 – 404.

Tew-Kai, E. and Marsac, F. (2009). Patterns of variability of sea surface chlorophyll in Mozambique Channel: A quantitative approach. Journal of Marine Systems, (77):77-88.

Rubrique

Social Network Analysis

Novel method to find directed community structures

based on triads cardinality

Gamgne Domgue Félicité

* _—

_{Tsopze Norbert}

* _—

_{René Ndoundam}

* * Computer Science Department - University of Yaounde I

BP 812 Yaounde - Cameroon

felice.gamgne@gmail.com, tsopze@uy1.uninet.cm, ndoundam@gmail.com

RÉSUMÉ.La détection des communautés est davantage un challenge dans les l’analyse des réseaux

orientés. Plusieurs algorithmes de détection de communautés ont été developpés et considèrent la relation entre les nœuds comme symmétrique, car ils ignorent l’orientation des liens, ce qui biaise les résultats en produisant des communnautés aléatoires. Ce document propose un algorithme plus eff cace, TRICA, basé sur l’extraction des kernels qui sont des ensembles de nœuds inf uents dans le réseau. Cette approche découvre des communautés plus signif catives avec une complexité tempo-relle meilleure que celles produites par certains algorithmes de détection de communautés de l’état de l’art.

ABSTRACT.Community structure extraction is once more a major issue in Social network analysis.

A plethora of relevant community detection methods have been implemented for directed graphs. Most of them consider the relationship between nodes as symmetric by ignoring links directionality during their clustering step, this leading to random results. This paper propose TRICA, an eff cient clustering method based on kernels which are inf uencial nodes, that takes into account the cardinality of triads containing those inf uencial nodes. To validate our approach, we conduct experiments on some networks which show that TRICA has better performance over some of the other state-of-the-art methods and uncovers expected communities.

MOTS-CLÉS :Réseaux orientés, détection des communautés kernel, Triade

1. Introduction

Community detection in directed networks appears as one of dominant research works in network analysis. The top meaning of community is a set of nodes that are densely connected with each other while sparsely connected with other nodes in the network [1]. This definition is interesting for undirected graphs ; like this many community detection algorithms implemented for directed networks simply ignore the directionality during the clustering step while other technics transform the directed graph into an undirected weigh-ted one, either unipartite or bipartite, and then algorithms for undirecweigh-ted graph clustering problem can be applied to them.

These simplistic technics are not satisfactory because the underlying semantic is not retained. For example, in a food web network, according to them, the community struc-ture will be corporated of predator species with their prays. This reflexion is not quite right. To make up for that idea, a generic definition of community detection consists of clustering nodes with homogeneous semantic characteristics(nodes centred around a set of objects owning the same interest). Our approach is based on extending the idea that within “good”communities, there are influencial nodes [6], kernels, that centralize infor-mation, so that it will easily be attainable. Influancial nodes are crossed by a maximal number of triads in a community. A triad is a set of3 nodes whose at least 2 are the

in-neighbor nodes (target vertices) of the3rd_{vertex, or according to the triadic closure.} Consequently, triads are the basis of many community structures [3]. Here we focus on the link orientation in triads. The specific contributions of our paper are :

– we mainly define a new concept named kernel degree to measure the strength of the pair of nodes and the similarity of vertices and give a new sense definition to kernel community based on the triadic closure.

– we develop a novel algorithm based on kernel degree to discover kernels and then communities from real social networks.

– We conduct to better quality improvement over the commmunity kernel detection algorithms.

The rest of paper is organized as follows. Section 2 is an introduction to related works. In Section 3, we formally define several concepts used into the proposed clustering me-thod. In Section 4, we develop the algorithm. Section 5 is experiment study and Section 6 concludes this study.

2. Related works

Most approaches focused on symmetric models which lose the semantics of link di-rections, a key factor that distinguishes directed networks from undirected networks. For detecting communities in directed networks [2], some studies propose a simple scheme that converts a directed graph into undirected one, this enabling to utilize the richness and complexity of existing methods to find communities in undirected graphs, thus, to mesure cluster strength, they use an objective function, the modularity. Yet, this mesure has a limit resolution [1]. More recently, various probabilistic models have been propo-sed for community detection [7]. Among them, stochastic block models are probably the most successful ones in terms of capturing meaningful communities, producing good per-formance, and offering probabilistic interpretations. However, its complexity is enough because in pratice, if the number of iterations goes beyond 20, the method discontinue

and results become insignificant. To make up for this complexity, some authors define “kernels”like described below.

A kernel is considered as a set of influencial nodes inside a group. It seems to be information centralizing nodes. Some methods explored the problem of detecting com-munity kernels, in order to either reduce the number of iterations, and consequently the time-complexity of algorithms defined for complex social networks or uncover the hid-den community structure in large social networks. [4] ihid-dentifies those influential members,

kernel and detects the structure of community kernels and proposed efficient algorithms

for finding community kernels. Through these algorithms, there is a random choice of the initial vertex, and the size of communities is fixed, leading to an arbitrary result estima-tion. To keep going, [3] proved that triangles(short cycles) play an important role in the formation of complex networks, especially those with an underlying community structure [5] and converts directed graph into an undirected and weighted one. This transformation misses the semantic of links. We propose a method which extracts triads based on Social properties to characterize the structure of real-world large-scale networks.

3. Method formalization

We propose in this section the kernel community model and introduce several related concepts and necessary notations.

3.1. Kernel community model

In directed networks, the link direction gives a considerable semantic to the graph and to the information flow. On twitter network for example, the notion of authority is pointed up as illustrated in Fig 1.(a), because of the relationship between a set of authoritative or hub blogs (nodesu and v ) and a set of non-popular one called followers (nodes x) as presented in Fig 1.(b) and Fig 1.(c).

We integrated this concept of authority as one concept named kernel degree. Fig 1.(a) is a visualization of an extract from a twitter network. Kernel communities consist of nodes owning the same “in-neighbourhood ”which corresponds to nodes that have more connections to the kernel (and not from the kernel) than a vertex outside the kernel. We consider only ingoing edges to the kernel vertices to express the strength these nodes get in some kind of network treated in this paper ; in a twitter network for example, hub blogs are viewed by many others followers and not the opposite ; in a citation network for example, authoritative authors like pioneers in a research area are more quoted by the others junior researchers. On the beginning, the kernel consists of two vertices sharing the same properties, leading to the notion of “triad ”which consists of the idea that two vertices of the kernel share the same friend, like defined in the following sub-section.

3.2. Basic terminology and concepts

Given a directed graphG(V, E) with n = |V | vertexes and m = |E| edges. Let Γube the neighborhood vertices set of vertexu. We now give some following useful definitions :

Definition 1 (Triad weight). Let the identifier of vertexx in G be j. The triad weight of any edge(u, v) in graph G can be represented as ∆. We can use T Wuvto represent the number of triads (triad cardinality) crossingu and v according to the scheme presented in the Fig 1.(b) and Fig 1.(c).

(a) Illustration of Twitter Net-work

(b) Closed triad (c) Opened triad

Figure 1. Basic structures of our kernel community model.

Definition 2 (Neighborhood overlap). Given two verticesu and v, let Γu be the set of vertices that are the neighborhood of vertexu, let Γv be the set of vertices that are the neighborhood of vertexv. Let N Ouv be the neighborhood overlap ofu and v. N Ouv= _|Γv∪Γu|Γv∩Γu|_|−2if there is an edge betweenu and v and 0 otherwise.

Definition 3 (The kernel degree). The Kernel degree of a pair of vertexu and v is :

Kuv = T Wuv∗ N Ouv.Kuvcan measure the strength of the pair(u, v) and the similarity

of nodes.

Definition 4 (New sense Kernel Community). A new definition of the kernel

commu-nity in the sense of this paper is a set of vertices with the same neighborhood such as these neighbors expand inward to the kernel, according the kernel degreeKuvgradually until its minimum.

Definition 5 (Triadic Closure). If two people in a social network have a friend in

common, then there is an increased likelihood that they will become friends themselves at some point in the future.

The algorithm is structured into two steps : detecting kernel communities and then migrating the others vertexes to the kernel to whom they are more connected to.

4. Our Method for extracting communities

The new algorithm is structured in two steps : identifying kernels, then migrating the other vertices to the kernel as described in the following subsections. The algorithm for extracting Kernel communities, TRICA (Triads Cardinality Algorithm ) we propose here makes use of a new concept Kernel degree, that measures the strength of a kernel gradually until it decreases. This concept is based on the triadic closure for emphasis the semantic proximity that links community members conducting to efficient propagation of information over the network. We focus on triads cardinality that is the number of neighboors two nodes own.

Data set Vertices Edges Types

Extract from Twitter Network 14 31 Directed

American Football Network 115 613 Undirected

Celegansneural 297 2359 Directed

4.1. TRICA algorithm

We assume that the network we want to analyze can be represented as a connected, di-rected, nonvalued graphG of n = |N | nodes and m = |E| edges. This step for identifying kernels is described in four sub-steps as follow :

1) Detect the in-central vertexv, which is the vertex with the maximal in-degree in the graph.

2) Determine the neighborhood overlap of each edge (u,v) through a variant of

Jaccard Index[1] represented byN Ouvas defined in Definition 2 3) Store neighboorhood verticesu of v like N Ouv> ε

4) ComputeKuvthrough the triad weightT Wuvas described in Definition 1. This action is repeated to measure the strength of a kernel gradually untilKuvdecreases.

These4 substeps are repeated n/k times, k being the in-degree of vertex v.

The space complexity of TRICA isO(n + m), and it runs in time more quickly than some of the state-of-the-art algorithms like shown in experiments.

The TRICA implementation for kernel communities is presented in Algorithm 1.

4.2. Deduction of global communities

After extracting kernels, it remains the other nodes which don’t belong to the kernels ; they are called non-kernels vertices. The process of generating global communities (com-munities containing both kernels and non-kernels vertices) consists of migrating the other members (belonging to a set called “auxiliary communities”) to the kernel whith whom they have a maximum number of connections, as described in Algorithm 2.

Algorithm 1 TRICA implementation for kernels extraction

Data: Directed graphG = (N, E) Result:K Kernels

1: Initialisation :K = ∅ ;

2: repeat

3: k = din_(v)/din_{(v) = max{d}in_{(t), ∀t ∈ V } ;}

4: CalculateN Ouvfor each(u, v) ∈ E ;

5: Γv[] ← {t ∈ V /∃t ∈ V, N Otv> 0, 8} ;Γv[].sort ;i ← 1 ; 6: S ← ∅ ; 7: j ← i ; u ← Γv[j] ;K∗ uv← 0 ; 8: repeat 9: ComputeKuv; 10: if(Kuv> K∗ uv) then 11: S ← S ∪ u ; 12: end if 13: u ← Γv[i + +] ; 14: until(Kuv< K∗ uv) ; 15: K ← K ∪ S ; 16:until (|V |/k) 17:ReturnK ;

5. Experiments

To study the effectiveness and accuracy of TRICA, we compare it with following comparative methods :

– NEWMAN : Method for finding community structure in directed networks using the betweenness based on modularity [6].

Algorithms Extract from Twitter American Football Celegansneural %∆ Comm Numb %∆ Comm Numb %∆ Comm Numb

Newmann 98% 2 39% 10 28% 194

Louvain 98% 2 63% 9 35% 5

Weba 98% 2 - 8 -

-Triad Cardinality 98% 2 70% 12 64% 21

Tableau 2. Community detection performance on the triad cardinality rate where the best

rate are in bold.

– LOUVAIN : Community detection algorithm based on modularity ; (we use Gephi tool for visualizing LOUVAIN results).

– WEBA [4] :Algorithm for community kernel detection in large social networks.

Algorithm 2 Algorithm implementation for non-kernels vertices migration

Data: Communities KernelsK = {K1, K2, ..., Kt} Result: Global CommunitiesGK= {G_K1, G_K2, ..., G_Kt}

LetN be set of auxiliary communities ; N = {N_K1, N_K2, ..., N G_Kt} ;

2: ∀i ∈ {1, ..., t}, GKi= ∅; repeat 4: ∀i ∈ {1, ..., t}, GKi= Ki∪ NKi; Fori ← 1 to t do 6: S ← {v /∈ ∪G_Ki/∀j ∈ {1, ..., t}}, |E(v, G_Ki)| ≥ |E(v, G_Kj)| > 0 ; 8: N_Ki← NKi∪ S ; G_Ki← Ki∪ NKi; 10: End For

until (No more vertices can be added)

12:ReturnGK;

Our method is evaluated on directed and undirected networks. We use two levels of evaluation : The first is based on the time complexity, and the second on the triad

car-dinality rate in communities, that is the percentage of communities in the partition with

highest triad cardinality rate. We use the function TCR defined as following, to evaluate our method :

T CR = Σi|∆i|_|∆|

wherei is one community and |∆| the number of triads.

When we apply TRICA on the data sets described in the table 1, results in Fig 2 are following : The Fig 2.(a) illustrates the2 expected communities of the Extract from Twit-ter Network, for all of the methods compared, with a triad cardinality rate in communities

of98% with kernels and followers [6]. But TRICA CPU time is better than other

me-thods CPU time, as shown if 2.(c) The table 2 summarizes the comparison with some state-of-the-art methods. It shows that Triad Cardinality algorithm provides the highest triad cardinality rate in communities. As far as the Football network is concerned, Triads cardinality algorithm can divide the network into12 communities exactly as shown in Fig 2.(b). In this result,8 communities are completely consistent, this revealed by the triad cardinality rate of70%. Meanwhile Newmann algorithm can divide it into 10 communi-ties and LOUVAIN into9. This number of communities does not reflect the real structure of the American College Football network. On the other hand, the result for applying

TRICA to Celegansneural network shown in Table2 presents that TRICA detects21 com-munities, while LOUVAIN detects5 and NEWMAN 194. But the triad cardinality rate is the best,64%, certifying that our method uncovers a better structure of social networks.

(a) Extract of Twitter Network (b) American College Football network.

(c) Efficiency comparison of TRICA and others algorithms on Twitter Network.

Figure 2. Results of applying TRICA to data sets.

6. Conclusion

In this paper, we focus on the problem of kernel community detection in directed graphs, kernels being the key tool for understanding the role of networks and its structure. We mainly interested on extracting kernels which are influential nodes on the network. Our kernel community model define triads according to some social properties to cha-racterize the structure of real-world large-scale network, and we develop a novel method based on the proposed new concept, the kernel degree which defines the strength of ker-nel community. Experiments proved that TRICA detects efficiently expected communities and achieves 20 % performance improvement over some other state-of-the-art algorithms, but it only works for unweighted graphs. Our next work is to optimize Triad

cardinality-based property, and adjust it to suit for detecting kernel communities from large-scale directed and weighted networks.

7. Bibliographie

[1] S. FORTUNATO, « Community detection in graphs », Physics Reports 486(3) 75-174, 2010. [2] F. D. MALLIAROSand M.VAZIRGIANNIS, « Clustering and community detection in directed

networks : A survey. », arXiv 1308.0971, 2013.

[3] C.KLYMKO, D.F GLEICHand T.G KOLDA, « Using Triangles to Improve Community De-tection in Directed Networks », Conference Stanford University.

[4] LIAORUOWANG, TIANCHENGLOU, JIETANGand JOHNE. HOPCROFT, « Detecting Com-munity Kernels in Large Social Networks ».

[5] A. PRAT-PÉREZ, D. DOMINGUEZ-SAL, J. M. BRUNATand J. L. LARRIBA-PEY, « Shaping communities out of triangles. », In CIKM 12 no

1677-1681, 2012.

[6] FÉLICITÉGAMGNEand NORBERTTSOPZE, « Communautés et rôles dans les réseaux sociaux », in : CARI ’14 : Proceedings of the 12th African Conference on Research in Computer science

and Applied Mathematics no

157 - 164, 2014.

[7] TIANBAOYANG, YUNCHI, SHENGHUOZHUand YIHONGGONGand RONGJIN,« Directed network community detection : A popularity and productivity link model. », In SIAM Data

Mining’10 no

A comparative study of three membrane

fouling models

Towards a generic model for optimization purposes

N. KALBOUSSI

a,*

J.HARMAND

b

N.BEN AMAR

a,**

F.ELLOUZE

a,***

a _{Département de chimie, Institut National des Sciences Appliquées et de Technologie (INSAT)}

Charguia, Tunis 1080, TUNISIE

Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur (LAMSIN)

b _{LBE, INRA, 11100, Narbonne, France}

jerome.harmand@supagro.inra.fr * nesrinekalboussi@gmail.com **nihel.benamar@insat.rnu.tn ***ellouze_fatma@yahoo.fr

ABSTRACT. Most of the published models of membrane fouling are too complex and contain too

many parameters to be estimated from experimental data. This works aims to justify the choice from the literature of a simple model of membrane fouling for control and optimization design purposes. To do so, we identify a simple and generic model from the literature and we show, using preliminary results, that this model can reproduce the same results than those much more complicated and specific published models with less parameters to estimate.

RÉSUMÉ. La plupart des modèles de colmatage de la membrane sont compliqués avec beaucoup

de paramètres à estimer à partir des données expérimentales. L'objectif de ce travail est de justifier le choix, à partir de la littérature, d'un model simple de colmatage de la membrane pour des fins de contrôle et d'optimisation. Pour ce faire, on identifie un modèle simple et générique et on montre que ce modèle peut reproduire les mêmes résultats que d'autres modèles publiés plus compliqués et spécifiques, avec moins de paramètres à estimer.

KEYWORDS: membrane bioreactor(MBR), fouling, modeling, mathematical models, optimization. MOTS-CLÉS : bioréacteur à membrane (BRM), colmatage, modélisation, modèles mathématiques,

1.

Introduction

The membrane bioreactors (MBR) are an increasingly used technology in wastewater treatment. Such a process combines a biological reactor with a filtration membrane that separates microorganisms and suspended matters from the purified water. The advantages are: a high quality effluent, a high solid retention time (SRT), a high possible biomass concentration and a small footprint. Despite its benefits and its widespread use, the MBR technology is constrained by membrane fouling. Fouling is due to the attachment of particles on membrane surface which leads to sever flux decline and an increase of the operating costs. Therefore, several authors have proposed different mathematical models to simulate the MBR process in order to be used in the prediction and control of membrane fouling. However, those models either include a lot of parameters to be estimated from experimental data and they are thus too complex to be really operational, or they make too many assumptions that limit their interest. In this paper, we propose to evaluate a simple generic mathematical model proposed by Benyahia et al. [1] by comparing this model to two other models published in the literature: the model of Pimentel et al. [2] and the model of Di Bella et al. [3]. In particular, we are interested in investigating the generic character of the model proposed by Benyahia et al. [1] for two purposes. The first is to illustrate its usefulness for control and optimization design purposes by justifying the high prediction capabilities of this model despite its simplicity. The second is to prove that if MBRs are very complex systems, yet they can be modeled by simple and generic mathematical models.

To do so, the models [2] and [3] are used as virtual processes to generate data that are then utilized to identify the model parameters of Benyahia et al. model [1] by using an optimization strategy. Model simulations and parameter estimation were conducted using Matlab.

2.

The model proposed by Pimentel et al.

Pimentel et al. [2] have proposed an integrated model coupling a biological model and a filtration model. The coupled model is formed of eight ordinary differential equations (ODEs) with six parameters to be estimated from experimental data. The biological model is designed using a simple chemostat reactor, involving one substrate and one biomass. The short-term evolution of the cake deposit on the membrane surface was modeled by equation (1) and the long-term evolution due to irreversible clogging was described by equation (2). In this model, the total resistance is calculated as the cake resistance while the intrinsic resistance of the membrane was neglected (equations (3) and (4)). The trans-membrane pressure can be determined according to equation (5).

For the relaxation phase, the model is represented by equations (6) to (7). The nomenclature used in the model is presented in Appendix 1.

- Coupled model for the filtration phase:

𝑚𝑚̇ = 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑚𝑚 𝑋𝑋 − 𝐽𝐽𝑎𝑎𝑎𝑎𝑝𝑝 𝜇𝜇𝑎𝑎𝑎𝑎𝑝𝑝 𝑚𝑚 (1)

𝛽𝛽 ̇ = − 𝛾𝛾 𝛽𝛽 (2)

𝑅𝑅𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑅𝑅𝑐𝑐𝑎𝑎𝑐𝑐𝑝𝑝 (3)

𝑅𝑅𝑐𝑐𝑎𝑎𝑐𝑐𝑝𝑝 = 𝜌𝜌 𝑚𝑚 + 𝑚𝑚_𝐴𝐴 0 (4)

𝑇𝑇𝑇𝑇𝑇𝑇 = 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑚𝑚_{𝐴𝐴 𝜂𝜂 𝑅𝑅}𝑡𝑡𝑡𝑡𝑡𝑡 (5)

- Coupled model for the relaxation phase :

𝑚𝑚̇ = − 𝐽𝐽𝑎𝑎𝑎𝑎𝑝𝑝 𝜇𝜇𝑎𝑎𝑎𝑎𝑝𝑝 𝑚𝑚 (6)

𝛽𝛽 ̇ = − 𝛾𝛾 𝛽𝛽 (7)

3. The model proposed by Di Bella et al.

The membrane bioreactor mathematical model of Di Bella et al. [3] consists of two sub-models. The biological activity is described in the first sub-model through twenty-six ODEs. This sub-model is a modified version of the well-know ASM1 [4] to consider the influence of the Soluble Microbial Products (SMPs), known as playing a key role in membrane fouling [5]. The cake layer formation was modeled by equation (10). The latter is regulated by two opposite phenomena: the suction which leads to attachment and the friction drag caused by the turbulent air flow. The attachment is proportional to the total suspended concentration as expressed by equation (8) while the friction drag is proportional to the local shear intensity as in equation (9). During backwashing phase, the detachment action of the cake layer is evaluated by equation (11) where 𝜂𝜂𝑐𝑐 is a calibrated parameter. The nomenclature used in Di Bella et al.'s model is given in Appendix 2.

- The model for the filtration phase:

𝑇𝑇𝑀𝑀𝑀𝑀𝑀𝑀 = 𝑎𝑎𝑀𝑀𝑀𝑀,𝑋𝑋𝐼𝐼 𝑋𝑋𝐼𝐼 + 𝑎𝑎𝑀𝑀𝑀𝑀,𝑋𝑋𝑀𝑀 𝑋𝑋𝑀𝑀 + 𝑎𝑎𝑀𝑀𝑀𝑀,𝐵𝐵𝐵𝐵 𝑋𝑋𝐵𝐵𝐵𝐵 + 𝑎𝑎𝑀𝑀𝑀𝑀,𝐵𝐵𝐴𝐴 𝑋𝑋𝐵𝐵𝐴𝐴 (8) 𝐺𝐺 = � 𝜌𝜌𝑀𝑀 𝑔𝑔 𝑄𝑄_𝜇𝜇 𝑎𝑎 𝑀𝑀 (9) 𝑇𝑇𝑠𝑠𝑠𝑠̇ = 24 𝑇𝑇𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑚𝑚 2 24 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑚𝑚 + 𝐶𝐶𝑑𝑑 𝑑𝑑𝑝𝑝 𝐺𝐺 − 𝛽𝛽 (1 − 𝛼𝛼)𝐺𝐺 𝑇𝑇𝑠𝑠𝑠𝑠2 𝛾𝛾 𝑉𝑉𝑠𝑠 𝑡𝑡𝑠𝑠+ 𝑇𝑇𝑠𝑠𝑠𝑠 (10)

𝑇𝑇𝑠𝑠𝑠𝑠̇ = − 𝜂𝜂𝑐𝑐 𝑇𝑇𝑠𝑠𝑠𝑠 (11) Di Bella et al. model includes forty-four parameters to be estimated from experimental data and it does not give equations to calculate the resistance of membrane fouling and thus the transmembrane pressure (TMP).

4. The model proposed by Benyahia et al.

Benyahia et al. [1] have proposed a simple model of membrane fouling and have connected it to a b iological process to demonstrate its utility in a large number of situations. In this model, two main fouling phenomena were considered: the attachment of solids onto the membrane surface (cake formation) and the retention of compounds inside the pores (pores clogging), in particular the SMP.

The coupled model of Benyahia et al. is formed of fourteen ODEs: ten ODEs to describe the biological activity and four ODEs to represent the filtration process, with twenty-six parameters. In their work, the authors [1] assume that total filtering membrane surface is not constant, contrary to many models of the literature. Instead, it is modeled by a decreasing function of both the mass of matter attached on the surface of the membrane m(t) and the mass of deposited matter into pores Sp(t) (notably SMP).

The dynamic of m(t) is proportional to the particulate matter (XT) and the total soluble

(STand SMP), as in equation (12). The evolution of Sp(t) is proportional to SMP (cf

equation 13). The filtration model of Benyahia et al. [1] is represented by the following dynamical equations and the nomenclature used in this model is given in Appendix 3:

- The model for the filtration phase:

𝑚𝑚̇ = 𝛿𝛿 𝑄𝑄𝑡𝑡𝑜𝑜𝑡𝑡 (𝐶𝐶𝑀𝑀 𝑀𝑀𝑇𝑇+ 𝐶𝐶𝑥𝑥 𝑋𝑋𝑇𝑇+ 𝐶𝐶𝑀𝑀𝑇𝑇𝑇𝑇 𝑀𝑀𝑇𝑇𝑇𝑇) − 𝑠𝑠𝑚𝑚 𝑚𝑚 (12)

𝑀𝑀𝑝𝑝̇ = 𝛿𝛿′ 𝑄𝑄𝑡𝑡𝑜𝑜𝑡𝑡(𝛽𝛽 𝑀𝑀𝑇𝑇𝑇𝑇 +_{15 (𝑀𝑀}𝛽𝛽 1+ 𝑀𝑀2)) (13)

𝑅𝑅𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑅𝑅0+ 𝛼𝛼 𝑚𝑚_{𝐴𝐴 + 𝛼𝛼}′ 𝑉𝑉𝑝𝑝_{𝜖𝜖 𝐴𝐴} 𝑀𝑀𝑝𝑝 (14)

𝑇𝑇𝑇𝑇𝑇𝑇 = 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑚𝑚_{𝐴𝐴 𝜂𝜂 𝑅𝑅}𝑡𝑡𝑡𝑡𝑡𝑡 (15)

- The model for the relaxation/backwashing phase:

𝑚𝑚 ̇ = − 𝜔𝜔 𝑚𝑚 (16)

5. Identification of Benyahia et al. 's model parameters using

Pimentel data

At this stage, Pimentel et al. model [2] is considered as a virtual process to generate data in order to identify the parameter of the model [1]. All the hypothesis considered in Pimentel et al. model [2] were applied to Benyahia et al. model [1]. Therefore, the parameter to be optimized of the model [1] are: δ Cx, 𝑠𝑠𝑚𝑚 , α and 𝜔𝜔.

The optimization of these parameters was done by the least squares method programmed with Matlab R2013a. The functional cost that was minimized is the sum of the error between the mass of attached matter calculated according to the model [1] and that determined according to the model [2] and the difference between the trans-membrane pressure calculated with the model [1] and that determined with the model [2]. It should be noticed here that in the model [1] the contribution of the SMP in the fouling was neglected in order to fit the hypothesis considered in [2].

The optimal values of the different parameters of the model [1] are presented in the table 1. The results of the simulation of the optimization problem are shown in the Figs.1 and 2. The comparison of the simulated data of the two models confirms the possibility of the model proposed by Benyahia et al. [1] to capture the mean value and the dynamics of the attached mass and the trans-membrane pressure.

Table 1 Optimal results for parameter estimation of the model [1] from the data of the

model [3]

Parameters Unit Value Lower bound Upper bound

δ CX dimensionless 1 0.9 1

𝑠𝑠𝑚𝑚 day-1 184.2 160 190

𝜔𝜔 day-1 _{184.2 160 190}

6. Identification of Benyahia et al. 's model parameters using

Di Bella data

In this part, the model of Di Bella et al.[3] was considered to evaluate the genericity of Benyahia et al. model [1]. To do that, the same approach as before was considered. The objective function that was minimized by the optimization problem is the difference between the mass of attached matter calculated according to the model [1] and that determined according to the model [3]. The optimal solution and the search ranges of the unknown parameters of Benyahia et al. model are presented in the table 2.

Figure 1. the accumulated mass on the membrane surface versus time